A particle moves along a straight line such t | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The displacement is given by $s = t^3 - 3t^2 + 2$.The velocity $v$ is the first derivative of displacement with respect to time: $v = \frac{ds}{dt

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(A) The displacement is given by $s = t^3 - 3t^2 + 2$.The velocity $v$ is the first derivative of displacement with respect to time: $v = \frac{ds}{dt} = 3t^2 - 6t$.The acceleration $a$ is the derivative of velocity with respect to time: $a = \frac{dv}{dt} = \frac{d^2s}{dt^2} = 6t - 6$.Set the acceleration to zero to find the time $t$:$6t - 6 = 0 \implies t = 1 \, s$.Now,substitute $t = 1 \, s$ into the displacement equation to find the displacement at that instant:$s = (1)^3 - 3(1)^2 + 2 = 1 - 3 + 2 = 0 \, m$.

Column-$I$	Column-$II$
$(1)$ Acceleration is positive	$(a)$ Speed of the particle decreases
$(2)$ Acceleration is negative	$(b)$ Speed of the particle increases
	$(c)$ Speed of the particle keeps changing

$A$ particle moves along a straight line such that its displacement at any time $t$ is given by $s = (t^3 - 3t^2 + 2) \, m$. The displacement when the acceleration becomes zero is ........ $m$.

Similar Questions

Match the items in Column-$I$ with the items in Column-$II$ correctly.

Column-$I$ Column-$II$

$(1)$ Acceleration is positive $(a)$ Speed of the particle decreases

$(2)$ Acceleration is negative $(b)$ Speed of the particle increases

$(c)$ Speed of the particle keeps changing

The correct position $(x)$ - time $(t)$ graph for a particle moving with negative acceleration is

$A$ particle starts from rest. Its acceleration $(a)$ versus time $(t)$ graph is as shown in the figure. The maximum speed of the particle will be.....$m/s$.

The velocity of a body depends on time according to the equation $v = \frac{t^2}{10} + 20$. The body is undergoing

The acceleration-time graph for a particle is given in the figure. If it starts motion at $t=0$, the distance travelled in $3 \, s$ will be ........... $m$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module